This application claims benefit of Japanese Patent application No. 2001-222961 filed in Japan Jul. 24, 2001, the contents of which are incorporated by this reference.
The present invention relates generally to an optical system and devices using the same, and more particularly to an optical system such as a viewing or image pickup optical system that is used with an image display device or the like which may be mounted over the head or face of an observer or added to cellar phones or easy-to-carry information terminals.
For the purposes of allowing individuals to enjoy large-screen images, image display devices, especially head or face-mounted type image display devices are now under increasing development. There is also a growing demand for providing large-screen viewing of image-wise or character-wise data on cellar phones or portable information terminals.
For instance, U.S. Pat. No. 2,993,319 proposes a vehicle-mounted display device using a reflection hologram element having functions similar to those of a beam splitter capable of reflecting and diffracting only light having a specific range of angles of incidence and transmitting light having other angles of incidence. As proposed and shown in this patent publication, the angle selectivity of the reflection hologram element is used to achieve the beam splitter function of guiding light from a light source to an observer.
A viewing optical system comprising a combination of a reflection hologram element formed on a spherical substrate in the air with a reflection hologram element formed on a planar substrate in the air is proposed in U.S. Pat. No. 4,874,214. In this case, the reflection hologram formed on the planar substrate makes use of angle selectivity, thereby achieving the beam splitter function.
The aforesaid U.S. Pat. No. 2,993,319 refers only to means for achieving a hologram beam splitter using the angle selectivity of a monochromatic (a single band: wavelength band) corresponding to the green wavelength region. For instance, this patent publication does not pay any attention to the case where, for instance, a beam splitter harnessing the angle selectivity of a reflection hologram element is designed for light in several (e.g., red (R), green (G) and blue (B) or three-band light) bands.
That patent publication does not also say anything specific about the profile, etc. of optical powers for achieving the beam splitter function making use of the angle selectivity of a reflection hologram element.
The viewing optical system proposed in U.S. Pat. No. 4,874,214 comprises a hologram element having a spherical shape. It is here noted that a hologram element has two powers, i.e., optical power due to a geometrical shape and optical power due to its diffraction effect. For instance, two powers of a hologram element formed on a substrate member of spherical shape are now explained with reference to FIGS. 27(a) and 27(b). The hologram element has power due to a difference in density between interference fringes as represented by the pitch of a periodical structure within the hologram element as shown in FIG. 27(a), and optical power due to its geometrical shape as shown in FIG. 27(b). Here assume R is the radius of curvature of the hologram substrate. Then, the optical power "PHgr" of a conventional optical refracting lens, and a conventional reflector may be calculated from the following equations:
"PHgr"=(nxe2x88x921)(1/R) for a refracting system
"PHgr"=2/R for a front surface mirror
"PHgr"=2n/R for a back-surface mirror
Here "PHgr" is the optical power due to the geometrical shape,
n is the refractive index of a medium, and
R is the radius of curvature of the hologram substrate.
It is thus understood that to obtain a certain quantity of optical power by the geometrical shape, the radius of curvature, R, of the back-surface mirror should be gentler than that of the front surface mirror by 1/n.
To put it another way, if the interior of the reflection hologram element is filled up with a medium with a refractive index n, for instance, a glass or plastic medium as is the case with a back-surface mirror, it is then possible to obtain large optical power due to geometrical shape, even when the geometrical shape has a gentle radius of curvature, R.
Thus, if an arrangement ensuring to generate large optical power at such a gentle radius of curvature R is used for an optical system, it is then possible to reduce aberrations produced at this hologram surface.
In the viewing optical system of U.S. Pat. No. 4,874,214 wherein the spacing between the planar surface and the spherical surface is not filled up with a glass or plastic medium, however, the geometrical shape must be constructed with a smaller radius of curvature R so as to obtain the required quantity of optical power by the geometrical configuration having a spherical shape.
When the geometrical shape is constructed with a smaller radius of curvature R, however, it is difficult to display satisfactory images because of increases in the aberrations produced at this reflecting surface. For lack of any optical surface in an optical path between the image plane and the aforesaid curved surface, it is difficult to make satisfactory correction for distortion.
Having been accomplished with a view of solving such problems with the prior art as described above, the primary object of the present invention is to provide a viewing or image pickup optical system used with image display devices, which system can be used with high efficiency at a plurality of wavelengths, enables bright images to be observed with high color reproducibility, is easy to assemble, resist to impacts such as vibrations, light in weight and compact in size, and makes it possible to observe images well corrected for aberrations, and devices using the same.
According to the first aspect of the present invention, the aforesaid object is achieved by the provision of an optical system that is disposed between an image plane and an optical pupil and having generally positive power, wherein:
said optical system comprises a first prism having a refractive index of greater than 1, a second prism having a refracting index of greater than 1, and a volume hologram element disposed between said first prism and said second prism and cemented thereto, wherein:
said volume hologram element comprises a first volume hologram optimized in such a way as to effect Bragg diffraction at least at a first wavelength and a second volume hologram optimized in such a way as to effect Bragg diffraction at a second wavelength different from said first wavelength, and said volume hologram element is designed in such a way that diffraction efficiency thereof reaches a maximum at a first angle of incidence and a first angle of reflection and diffraction which vary with the position of said volume hologram element at least at said first wavelength and at a second angle of incidence and a second angle of reflection and diffraction which vary with the position of said volume hologram element at least at said second wavelength (it is here noted that the volume hologram element includes an element obtained by multi-exposing a single-layer volume hologram film to light including a plurality of wavelengths or a multilayer hologram element, and that the first and second wavelengths refer to two wavelengths in the RGB wavelength region or, for instance, two wavelengths R1 and R2 chosen out of the R wavelength region of the RGB wavelength region),
said first prism is located on said optical pupil side and said second prism is located on said image plane side,
said second prism has at least one reflecting surface formed at a surface thereof different from a surface thereof having said volume hologram element,
a light beam, which propagates from said optical pupil to said image plane in a forward or backward direction and includes at least a ray component of said first wavelength and at least a ray component of said second wavelength, passes through said volume hologram element in order from said first prism side to said second prism side, whereupon said light beam is reflected at said reflecting surface in said second prism and reflected and diffracted by said volume hologram element in said second prism, and
said first volume hologram and said second volume hologram are identical with each other in terms of interference fringe shape and spacing on the surfaces thereof but are difference from each other in terms of interference fringe spacing and tilt in hologram media.
Why the aforesaid arrangement is used in the present invention, and how it works is now explained.
The optical system of the present invention is disposed between the image plane and the optical pupil, and has generally positive power. For backward ray tracing, a light beam passing from the optical pupil to the image plane is selected, and for forward ray tracing, a light beam passing from the image plane to the optical pupil is selected. When a light beam is passed in the forward ray tracing direction while an image display element is located at the image plane and the pupil of the eye of an observer is placed in the vicinity of the position of the optical pupil, the optical system may be used as a viewing or eyepiece optical system. When a light beam from a subject positioned in front of the optical pupil is passed in the backward ray tracing direction while an image pickup element such as a silver salt film or CCD is located at the image plane, the optical system may be used as an image pickup optical system.
Disposed between the image plane and the optical pupil and having generally positive power, the optical system of the present invention comprises a first prism having a refractive index of greater than 1, a second prism having a refractive index of greater than 1 and a volume hologram element disposed between the first prism and the second prism and cemented thereto. The first prism is positioned on the optical pupil side. The second prism is positioned on the image plane side, and has at least one reflecting surface formed at a surface thereof different from the surface thereof having the volume hologram element.
The volume hologram element may be a multi-recorded or multi-layered hologram element. The volume hologram element comprises a first volume hologram optimized in such a way as to effect Bragg diffraction at least at a first wavelength and a second volume hologram optimized in such a way as to effect Bragg diffraction at a second wavelength different from the first wavelength, and should be designed in such a way that the diffraction efficiency reaches a maximum at a first angle of incidence and a first angle of reflection and diffraction that vary with the position of the volume hologram element at at least the first wavelength and at a second angle of incidence and a second angle of reflection and diffraction that vary with the position of the volume hologram element at at least the second wavelength.
Such a volume hologram element, for instance, may include an element formed by multi-exposure of a single-layer volume hologram film to a plurality of wavelengths (multi-recording) or a multilayer hologram element formed by recording holograms of different wavelengths on a plurality of layers, one wavelength for one layer. The first and second wavelengths are understood to refer to two wavelengths chosen from the RGB wavelength bands or two wavelengths R1 and R2 chosen from, for instance, the R region in the RGB wavelength band.
The optical system of the present invention is designed in such a way that a light beam, which propagates from the optical pupil to the image plane in a forward or backward direction and includes at least a ray component of the first wavelength and at least a ray component of the second wavelength, passes through the volume hologram element in order from the first prism side to the second prism side, whereupon the light beam is reflected at the reflecting surface in the second prism and reflected and diffracted by the volume hologram element in the second prism.
Thus, the interior of the optical system is filled up with the glass, plastic or other materials for the first prism, second prism and volume hologram element, whereby the optical power due to the surface shape of each optically active surfaces can be increased with satisfactory correction for aberrations such as spherical aberrations and coma.
In the optical system of the present invention, the volume hologram element is interposed between the first prism and the second prism, and cemented to both prisms.
If a volume hologram element is used as a beam splitter positioned at the boundary between the first prism and the second prism for branching an optical path, diffraction efficiency approximate to 100% can then be obtained upon reflection and diffraction with no substantial transmission loss, so that bright image display and image pickup can be achieved with no light quantity losses. If two prisms, i.e., the first prism on the optical pupil side and the second prism on the image plane side are integrated with a volume hologram element sandwiched between them into a one-piece member, it is then possible to eliminate any optical axis misalignment due to the presence of an air spacing upon assembling or troublesome setting operation. It is thus possible to achieve a viewing or image pickup system that is easy to assemble and resistant to impacts such as vibrations.
If the volume hologram element is cemented to the first and second prisms while it is sandwiched between them, it is then possible to make the volume hologram element dust-proof. It is thus possible to prevent enlarged observation of dust, etc. and transfer of them onto the image plane without recourse to any separate dust-proof member, and penetration of moisture from outside into the volume hologram element, which may otherwise cause the volume hologram to expand, resulting in a change of the peak wavelength of diffraction efficiency.
In the optical system of the present invention, the first volume hologram and the second volume hologram should be identical with each other in terms of their surface interference shape and spacing but should be different from each other in terms of the interference fringe spacing and tilt in their hologram media.
Why that arrangement is critical for the present invention is now explained.
For a better understanding, here consider a volume hologram element 6 which is made up of three volume hologram layers 6R, 6G and 6B stacked one upon another, as shown in FIG. 8(a). Then assume that the volume hologram 6R is optimized in such a way as to effect Bragg diffraction at a specific wavelength in the R wavelength region, the volume hologram 6G is optimized in such a way as to effect Bragg diffraction at a specific wavelength in the G wavelength region, and the volume hologram 6B is optimized in such a way as to effect Bragg diffraction at a specific wavelength in the B wavelength region.
A volume hologram has the property of having the maximum diffraction efficiency at an optimized wavelength in such a way that Bragg diffraction takes place. Even at other wavelengths, however, that volume hologram generally has a diffraction efficiency depending on a shift from the optimized wavelength. Accordingly, when light having a specific wavelength in the B wavelength region, upon incidence on a specific position A in the volume hologram element 6 at an angle of incidence iB optimized at that position A, is diffracted by the volume hologram 6B in the volume hologram 6 at an angle of diffraction rB with the maximum efficiency to produce diffracted light 21B, the incident light 20B is slightly, if not largely, diffracted by other volume holograms 6R and 6G to produce diffracted light 21BR and 21BG, as shown in FIG. 8(a). Then, the angles of diffraction rBR and rBG of diffracted light 21BR and 21BG having specific wavelengths in the B wavelength region are generally different from the angle of diffraction rB due to the volume hologram 6B. Thus, when the same wavelength (i.e., the specific wavelength in the B wavelength region) is diffracted by the volume hologram 6 in a plurality of different directions, the image-formation capability of an optical system, which uses such a volume hologram element 6 as a beam splitter and to which the present invention is applied, becomes worse (leading to not only chromatic aberrations but also monochromatic aberration).
To prevent any diffraction of light of one such wavelength in plural directions according to the present invention, the surfaces of the volume holograms 6R, 6G and 6B forming the volume hologram element 6 should be constructed of interference fringes having the same shape and spacing, so that the angles of diffraction rBR and rBG in FIG. 8(a) become the same as the angle of diffraction rB and, hence, each of the diffracted light 21BR and 21BG is in coincidence with the diffracted light 21B, as shown in FIG. 8(b). Consequently, incident light having any desired wavelength is diffracted with a specific angle of diffraction at any desired position in the volume hologram element 6; diffraction of light having any desired wavelength in plural directions is prevented.
It is here understood that the angle of diffraction of light diffracted by a volume hologram is determined by the shape and spacing of interference fringes on its surface or if the volume holograms 6R, 6G and 6B forming the volume hologram 6 are identical with one another in terms of their surface interference fringe shape and spacing, the three volume holograms 6R, 6G and 6B have the same angle of diffraction, as explained just below.
Consider a volume hologram sandwiched between isotropically uniform media, as shown in FIG. 9. A region I is defined by the isotropically uniform medium on the entrance side, a region II is defined by the volume hologram and a region II is defined by the isotropically uniform medium on the transmission side, with x- and z-axes determined as shown.
A diffraction grating recorded in a phase type volume hologram may be given by
xcex5=xcex5II+xcex94xcex5xc2x7cos(Kxc2x7r)xe2x80x83xe2x80x83(11) 
where eII is the average dielectric constant of the hologram, xcex94e is the amplitude of dielectric constant modulation of the hologram, r is a position vector, and K is a grating vector that may be represented by
K=2xcfx80/xcex9(sin xcfx86, 0, cos xcfx86)xe2x80x83xe2x80x83(12) 
Here xcex9 is a grating spacing (interference fringe spacing), and xcfx86 is the angle of K with the z-axis. It is noted that (sin xcfx86, 0, cos xcfx86) represents that the x component is sin xcfx86, the y component is 0, and the z component is a vector of cos xcfx86, as hereinafter applies.
With respect to S-polarized light, a wave equation in the hologram is given by
∇2E+k2xcex5E=0xe2x80x83xe2x80x83(13) 
Here E is an electric field, and k is the magnitude of a wave vector in vacuum, given by
k=2xcfx80/xcex
For reason of the periodicity of the grating (interference fringes), Floquet""s theorem may hold; the electric field E in the hologram may be given by
E=xcexa3S1(z)exp(xe2x88x92j"sgr"1xc2x7r)xe2x80x83xe2x80x83(15) 
i
"sgr"i=xcfx81xe2x88x92iKxe2x80x83xe2x80x83(16) 
where j is an imaginary unit, and xcfx81 is the wave vector of reference light (zero-order diffracted light), i is an integer tantamount to the order of diffraction in the case of a hologram, S1(z) is the amplitude of an i-th order diffracted light, and "sgr"i is the wave vector of an i-th order diffracted light.
Alternatively, xcfx81 may be represented by
xcfx81=2xcfx80/xcexxc3x97{square root over ( )}xcex5II(sin xcex8, 0, cos xcex8)xe2x80x83xe2x80x83(17) 
Here xcex8 is the angle of incidence of reference light (zero-order light) in the hologram.
Regarding the i-th diffracted light emerging from the hologram, the hologram surface tangential component of the wave vector must be preserved according to phase matching conditions, as given by the following equation:
kIixc2x7x0="sgr"ixc2x7x0=kIIIixc2x7x0xe2x80x83xe2x80x83(18) 
Here kIi and kIIIi are the wave vectors of the i-th order diffracted light upon reflection and transmission outside of the hologram, respectively, and x0 is a unit vector in the x-axis direction.
From equations (12), (16) and (17), the second term of equation (18) is
"sgr"ixc2x7x0=2xcfx80/xcexxc3x97{square root over ( )}xcex5IIxc3x97sin xcex8xe2x88x92i2xcfx80/xcex9xc3x97sin xcfx86xe2x80x83xe2x80x83(19) 
Since the grating (interference fringes) spacing xcex9s is
xcex9s=xcex9/sin xcfx86xe2x80x83xe2x80x83(20) 
equation (19) may be rewritten as
"sgr"ixc2x7x0=2xcfx80/xcexxc3x97{square root over ( )}xcex5IIxc3x97sin xcex8xe2x88x92i2xcfx80/xcex9sxe2x80x83xe2x80x83(21) 
In region I formed of the isotropically uniform medium, the magnitude of the wave vector of diffracted light is represented by
|kI1|=2xcfx80/xcexxc3x97{square root over ( )}xcex5Ixe2x80x83xe2x80x83(22) 
Here xcex5I is the dielectric constant of region I.
Therefore, the z-component of the wave vector of diffracted light in region I is                                                                                           k                  Ii                                ·                                  z                  0                                            =                              xe2x80x83                            ⁢                                                {                                                                                    "LeftBracketingBar"                                                  k                          Ii                                                "RightBracketingBar"                                            2                                        -                                                                  (                                                                              σ                            i                                                    ·                                                      x                            0                                                                          )                                            2                                                        }                                                  1                  /                  2                                                                                                        =                              xe2x80x83                            ⁢                                                -                                      "LeftBracketingBar"                                          k                      Ii                                        "RightBracketingBar"                                                  ⁢                                                      {                                          1                      -                                                                        1                          /                                                      ϵ                            1                                                                          xc3x97                                                                              (                                                                                                                            √                                                                      ϵ                                    II                                                                                                  xc3x97                                sin                                ⁢                                                                  xe2x80x83                                                                ⁢                                θ                                                            -                                                              i                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  λ                                  /                                  Λ                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                s                                                                                      )                                                    2                                                                                      }                                                        1                    /                    2                                                                                                          (        23        )            
so that the wave vector in region I is given by                               k          Ii                =                  2          ⁢                      π            /            λ                    xc3x97                      √                          ϵ              I                                xc3x97                      (                                                            1                  /                                      √                                          ϵ                      I                                                                      xc3x97                                  (                                                                                    √                                                  ϵ                          II                                                                    xc3x97                      sin                      ⁢                                              xe2x80x83                                            ⁢                      θ                                        -                                          i                      ⁢                                              xe2x80x83                                            ⁢                                              λ                        /                        Λ                                            ⁢                                              xe2x80x83                                            ⁢                      s                                                        )                                            ,              0              ,                              -                                                      {                                          1                      -                                                                        1                          /                                                      ϵ                            I                                                                          xc3x97                                                                              (                                                                                                                            √                                                                      ϵ                                    II                                                                                                  xc3x97                                sin                                ⁢                                                                  xe2x80x83                                                                ⁢                                θ                                                            -                                                              i                                ⁢                                                                  xe2x80x83                                                                ⁢                                                                  λ                                  /                                  Λ                                                                ⁢                                                                  xe2x80x83                                                                ⁢                                s                                                                                      )                                                    2                                                                                      }                                                        1                    /                    2                                                                        )                                              (        24        )            
Here z0 is a unit vector in the z-axis direction.
The wave vector in region III, too, is likewise given by                               k          IIIi                =                  2          ⁢                      π            /            λ                    xc3x97                      √                          ϵ              III                                xc3x97                      (                                                            1                  /                                      √                                          ϵ                      III                                                                      xc3x97                                  (                                                                                    √                                                  ϵ                          II                                                                    xc3x97                      sin                      ⁢                                              xe2x80x83                                            ⁢                      θ                                        -                                          i                      ⁢                                              xe2x80x83                                            ⁢                                              λ                        /                        Λ                                            ⁢                                              xe2x80x83                                            ⁢                      s                                                        )                                            ,              0              ,                                                {                                      1                    -                                                                  1                        /                                                  ϵ                          III                                                                    xc3x97                                                                        (                                                                                                                    √                                                                  ϵ                                  II                                                                                            xc3x97                              sin                              ⁢                                                              xe2x80x83                                                            ⁢                              θ                                                        -                                                          i                              ⁢                                                              xe2x80x83                                                            ⁢                                                              λ                                /                                Λ                                                            ⁢                                                              xe2x80x83                                                            ⁢                              s                                                                                )                                                2                                                                              }                                                  1                  /                  2                                                      )                                              (        25        )            
Equations (24) and (25) indicate that the wave vector of diffracted light emerging from the phase type volume hologram is dependent on its surface grating spacing rather than on the three-dimensional structure of the grating (interference fringes).
It is thus understood that as is the case with a thin hologram, the direction of diffraction of light emerging from the phase type volume hologram is determined by the grating (interference fringes) spacing on its surface.
For P-polarized light, the wave equation in the hologram with respect to a magnetic field H is written as follows:
∇2Hxe2x88x92(∇xcex5/xcex5xc3x97∇)H+k2xcex5H=0xe2x80x83xe2x80x83(26) 
If, as is the case with S-polarized light, Floquet""s theorem is used, then the magnetic field H in the hologram may be represented as
H=xcexa3U1(z)exp(xe2x88x92j"sgr"1xc2x7r)xe2x80x83xe2x80x83(27) 
i
Here U1(z) is the magnitude of an i-th diffracted light at the magnetic field.
For the P-polarized light, too, it is understood that as is the case with the S-polarized light, an i-th diffracted light emerging from the hologram has a hologram surface tangent component of its wave vector preserved according to phase matching conditions, and wave vectors in regions I and III are the same as those given by equations (24) and (25), so that the direction of diffraction of light is determined by the grating (interference fringes) spacing on the surface of the hologram.
For an amplitude type hologram, too, electromagnetic waves propagating therethrough may be described as in equations (15) and (27) according to Floquet""s theorem.
Accordingly, the direction of diffraction of light is determined by the grating (interference fringes) spacing on the hologram surface as is the case with the phase type volume hologram.
It is thus found that as is the case with a thin hologram, the direction of diffraction of light by the volume hologram is determined by the interference fringe spacing on the hologram surface rather than by the three-dimensional structure of the grating (interference fringes).
It is here noted that the holograms are identical with one another in terms of interference fringe shape and spacing includes not only the case where they are identical with one another at the same place but also cases where the tilts of interference fringes vary within the range of xc2x15xc2x0, preferably xc2x11xc2x0, and the spacing of interference fringes vary within the range of xc2x15%, preferably xc2x11%.
With the optical system of the present invention wherein the interior thereof is filled with a transparent medium having a refractive index of greater than 1, for instance, glass or plastic material, the optical power defined by the reflecting surface and the reflection hologram plane upon reflection can be ensured at an ever gentler radius of curvature, R. It is thus possible to reduce, or make satisfactory correction for, aberrations produced at each reflecting surface. Since the interior of the optical system is constructed of a transparent medium having a refractive index of greater than 1, a refracting surface is positioned in front of the image plane, so that satisfactory correction of distortion can be made.
Preferably in the optical system of the present invention, the first and second prisms should be formed of the same type medium.
It is also preferable that the shape of the surface of the first prism to which the volume hologram element is cemented is substantially the same as the shape of the surface of the second prism to which the volume hologram element is cemented.
It is here noted that the phrase xe2x80x9csubstantially the samexe2x80x9d implies that surface shape differences within the margin of errors on production are permissible.
Generally in the optical system of the present invention, the volume hologram element is a film type plane hologram. The surface of the first prism that is one substrate to which the plane hologram element is applied, and the surface of the second prism that is another substrate to which the plane hologram element is applied, should be in a planar or cylindrical form.
Here reference is made to specific embodiments of what arrangements the surfaces of the first and second prisms are positioned in. Some examples will be given later. As viewed in order of a ray propagating from the optical pupil to the image plane, the first prism should preferably comprise, at least, a first entrance surface for entering a ray from the optical pupil into the first prism and a first exit surface through which the ray leaves the first prism with a first prism medium filled between them. The second prism should preferably comprise, at least, a first entrance surface for entering the ray emerging from the first prism into the second prism, a reflecting surface for reflecting the ray within the second prism and a second exit surface through which the ray leaves the second prism, with a second prism medium filled between them. Preferably in the second prism, that reflecting surface should be configured in such a concave curved shape as to give positive power to the ray on reflection.
It is then preferable that the first entrance surface of the first prism in the optical system of the present invention is configured in such a curved shape as to give power to the ray on transmission, and the second exit surface of the second prism is configured in such a curved shape as to give power to the ray on transmission.
Preferably in the optical system of the present invention, a ghost light removal member for preventing the ghost light from striking on the eyeball of an observer should be provided on an optically inactive surface of the first and second prisms other than the optically active surfaces for transmitting and reflecting light rays.
When the second exit surface of the second prism is defined as the upper surface, it is effective to provide such ghost light removal members on the bottom and side of the optical member. The xe2x80x9coptically active surfacexe2x80x9d also includes areas outside of the effective ray diameter in the second exit surface, outside of the effective ray diameter in the reflecting surface of the second prism, and outside of the effective ray diameter in the first entrance surface of the first prism. It is also effective to provide such members at these areas.
Preferably in the optical system of the present invention, the rotationally asymmetric curved shape of the first entrance surface has an action on correction of rotationally asymmetric aberrations.
Preferably in the optical system of the present invention, the rotationally asymmetric curved shape of the first entrance surface of the first prism is constructed of a free-form surface having only one symmetric plane that should preferably be in coincidence with the turn-back plane (Y-Z plane) of the optical axis.
Preferably in the optical system of the present invention, the shape of the second exit surface of the second prism is a rotationally asymmetric free-from shape.
Thus, if the transmitting surface (the second exit surface of the second prism) is positioned at the front surface of an image display element (in the case of a viewing optical system with the image display element disposed at the image plane while a light beam propagates in the backward direction from the optical pupil to the image plane) or an image pickup element (in the case of an image pickup optical system with the image pickup element located at the image plane while a light beam propagates in the forward direction from the optical pupil to the image plane), it is then possible to make satisfactory correction for distortions. It is noted that while the front surface of this image display element or image pickup element may be constructed of a rotationally symmetric shape, it is more preferable to have recourse to a free-form surface so as to correct decentration aberrations occurring when optically active surfaces are decentered for the purpose of slimming down the optical system.
Preferably in the optical system of the present invention, the rotationally asymmetric curved shape of the second exit surface of the second prism is constructed of a free-form surface having only one symmetric plane that should preferably be in coincidence with the turn-back plane (Y-Z plane) of the optical axis.
In the present invention, while the surfaces forming the first prism and the surfaces forming the second prism should preferably be constructed of rotationally asymmetric surfaces such as free-form surfaces for the purpose of achieving an optical system having satisfactory telecentric properties with well-corrected rotationally asymmetric distortions, it is understood that they may be constructed of rotationally symmetric surfaces such as spherical, and aspheric surfaces or, alternatively, anamorphic surfaces.
Preferably in the optical system of the present invention, chromatic aberrations of magnification of both the rotationally symmetric component and the rotationally asymmetric component are corrected by allowing the volume hologram element to reflect and diffract light rays.
Thus, correction of chromatic aberrations of magnification of both the rotationally symmetric component and the rotationally asymmetric component with the reflection volume hologram element ensures high contrasts.
In order to take advantage of the angle selectivity of a reflection volume hologram element thereby achieving the beam splitter function, it is desired for the optical system of the present invention to satisfy at least one of the following conditions (1) and (2):
xe2x88x920.20 less than PX4/PX less than 0.50xe2x80x83xe2x80x83(1) 
xe2x88x920.20 less than PY4/PY less than 0.30xe2x80x83xe2x80x83(2) 
Here assume that the direction of an axial chief ray passing through the center of the optical pupil is the Z-axis direction, the decentration direction of the optical system and optical surfaces is the Y-axis direction and the direction perpendicular to the Y-axis and Z-axis is the X-axis direction, and let xcex4y indicate the angle of a ray leaving the optical system with respect to an axial chief ray upon projected onto the Y-Z plane with the proviso that said ray leaves the optical system when a ray having a minute height, d, is entered from the optical pupil side into the Y-Z plane parallel with the axial chief ray, xcex4y/d indicate the power, PY, of the optical system in the Y-direction, xcex4x indicate the angle of a ray leaving the optical system with respect to an axial chief ray upon projected onto a plane perpendicular to the Y-Z plane and including that axial chief ray with the proviso that said ray leaves the optical system when a ray having a minute height, d, is entered from the optical pupil side into the X-Z plane parallel with the axial chief ray, and xcex4x/d indicate the power, PX, of the optical system in the X direction. Likewise, assume that PY4 and PX4 are the powers of the reflecting surface in the second prism forming part of the optical system in the Y and X directions, respectively.
When the values of the aforesaid conditions (1) and (2) are less than the lower limits of xe2x88x920.20, the optical power of the decentered reflecting surface becomes too large in a negative direction to correct decentration aberrations produced at that reflecting surface. There are also large variations in the angle of incidence of light rays on the reflection hologram plane upon transmission, resulting in multiple diffraction. Consequently, it is difficult to display high-definition images or the volume hologram element fails to function as a beam splitter.
When the values of the aforesaid conditions (1) and (2) are greater than the respective upper limits of 0.50 and 0.30, the optical power of the decentered reflecting surface becomes too large in a negative direction to correct decentration aberrations produced at that reflecting surface. There are also large variations in the angle of incidence of light rays on the reflection hologram plane upon transmission, resulting in multiple diffraction. Consequently, it is difficult to display high-definition images or the volume hologram element fails to function as a beam splitter.
More preferably, the optical system of the present invention should satisfy at least one of the following conditions (1-1) and (2-1):
0.00 less than PX4/PX less than 0.35xe2x80x83xe2x80x83(1-1) 
xe2x88x920.10 less than PY4/PY less than 0.20xe2x80x83xe2x80x83(2-1) 
The lower and upper limits to these conditions have the same meanings as described above.
Even more preferably, the optical system of the present invention should satisfy at least one of the following conditions (1-2) and (2-2):
0.15 less than PX4/PX less than 0.25xe2x80x83xe2x80x83(1-2) 
0.00 less than PY4/PY less than 0.10xe2x80x83xe2x80x83(2-2) 
The lower and upper limits to these conditions have the same meanings as described above.
In Example 1 given later, the values of these conditions are as follows.
PX4/PX=0.190 
PY4/PY=0.045 
The optical system of the present invention may also be embodied as a viewing optical system comprising a two-dimensional image display element disposed at the image plane, so that an image on the two-dimensional image display element can be observed on an enlarged scale.
For instance, this embodiment may be a head-mounted type image display device comprising a body portion built in as the viewing optical system, a support member for supporting said body portion over the head of an observer in such a way that the optical pupil of the viewing optical system is kept at the eyeball position of the observer, and a speaker member for transmitting sounds to the ear of the observer.
Alternatively, that body portion may comprise a viewing optical system for the right eye and a viewing optical system for the left eye, and that speaker member may comprise speaker means for the right ear and speaker means for the left ear. In this case, an earphone may be used as that speaker member.
The optical system of the present invention may be applied not only to viewing systems but also to image pickup systems. An image pickup system may have an image pickup element disposed at the image plane, so that object light can be entered from the optical pupil side into the image pickup system to pick up an object image.
It is here noted that the axial chief ray for a viewing optical system is defined by backward tracing of a light ray passing through an optical pupil center forming an exit pupil and arriving at the center of a two-dimensional image display element, and the axial chief ray for an image pickup optical system is defined by forward tracing of a light ray passing through an optical pupil center forming an aperture stop and arriving at the center of an image pickup element. Then, the optical axis is defined by a straight line form of axial chief ray leaving the center of the exit pupil or aperture stop and intersecting as far as the first entrance surface of the first prism and the Z-axis is defined by this optical axis. The Y-axis is defined by an axis perpendicular to the Z-axis and found in the decentered planes forming the first prism, and an axis perpendicular to the Z-axis and the Y-axis is defined as the X-axis. The center of the exit pupil or aperture stop is defined as the origin of a coordinate system for the viewing or image pickup optical system of the present invention. In the present invention, the surface numbers are given according to the backward ray tracing from the exit pupil toward the two-dimensional image display element or according to the forward ray tracing from the aperture stop toward the image pickup element. The direction of the axial chief ray propagating from the exit pupil to the two-dimensional image display element or from the aperture stop to the image display element is defined as the positive direction of the Z-axis, the direction of the Y-axis toward the two-dimensional image display element or toward the image pickup element as the positive direction of the Y-axis, and the direction of the X-axis forming a right hand system with the Y-axis and Z-axis as the positive direction of the X-axis.
Here the free-form surface used herein is defined by the following equation (a). It is noted that the Z-axis of this defining equation provides the axis of the free-form surface.                     Z        =                              c            ⁢                          xe2x80x83                        ⁢                                          r                2                            /                              [                                  1                  +                                      √                                          {                                              1                        -                                                                              (                                                          1                              +                              k                                                        )                                                    ⁢                                                      c                            2                                                    ⁢                                                      r                            2                                                                                              }                                                                      ]                                              +                                    ∑                              j                =                2                            ∞                        ⁢                                          C                j                            ⁢                              X                m                            ⁢                              Y                n                                                                        (        a        )            
In equation (a), the first term is a spherical term and the second term is a free-form surface term.
In the spherical term,
c is the curvature of the apex,
k is a conic constant (conical constant), and
r={square root over ( )}(X2+Y2)
The free-form term is                     Z        ∞                    j        =        2              ⁢          C      j        ⁢          X      m        ⁢          Y      n        =                    C        2            ⁢      X        +                  C        3            ⁢      Y        +                  C        4            ⁢              X        2              +                  C        5            ⁢      XY        +                  C        6            ⁢              Y        2              +                  C        7            ⁢              X        3              +                  C        8            ⁢              X        2            ⁢      Y        +                  C        9            ⁢      X      ⁢              xe2x80x83            ⁢              Y        2              +                  C        10            ⁢              Y        3              +                  C        11            ⁢              X        4              +                  C        12            ⁢              X        3            ⁢      Y        +                  C        13            ⁢              X        2            ⁢              Y        2              +                  C        14            ⁢      X      ⁢              xe2x80x83            ⁢              Y        3              +                  C        15            ⁢              Y        4              +                  C        16            ⁢              X        5              +                  C        17            ⁢              X        4            ⁢      Y        +                  C        18            ⁢              X        3            ⁢              Y        2              +                  C        19            ⁢              X        2            ⁢              Y        3              +                  C        20            ⁢      X      ⁢              xe2x80x83            ⁢              Y        4              +                  C        21            ⁢              Y        5              +                  C        22            ⁢              X        6              +                  C        23            ⁢              X        5            ⁢      Y        +                  C        24            ⁢              X        4            ⁢              Y        2              +                  C        25            ⁢              X        3            ⁢              Y        3              +                  C        26            ⁢              X        2            ⁢              Y        4              +                  C        27            ⁢      X      ⁢              xe2x80x83            ⁢              Y        5              +                  C        28            ⁢              Y        6              +                  C        29            ⁢              X        7              +                  C        30            ⁢              X        6            ⁢      Y        +                  C        31            ⁢              X        5            ⁢              Y        2              +                  C        32            ⁢              X        4            ⁢              Y        3              +                  C        33            ⁢              X        3            ⁢              Y        4              +                  C        34            ⁢              X        2            ⁢              Y        5              +                  C        35            ⁢      X      ⁢              xe2x80x83            ⁢              Y        6              +                  C        36            ⁢              Y        7            
Here Cj (j is an integer of 2 or greater) is a coefficient with the proviso that j={(m+n)2+m+3n}/2+1 (m and n are each an integer of greater than 0).
In general, the aforesaid free-form surface has no symmetric surface at both the X-Z plane and the Y-Z plane. However, by reducing all the odd-numbered terms for X to zero, that free-form surface can have only one symmetric surface parallel with the Y-Z plane. For instance, this may be achieved by reducing to zero the coefficients for the terms C2, C5, C7, C9, C12, C14, C16, C18, C20, C23, C25, C27, C29, C31, C33, C35, . . . .
By reducing all the odd-numbered terms for Y to zero, the free-form surface can have only one symmetric surface parallel with the X-Z plane. For instance, this may be achieved by reducing to zero the coefficients for the terms C3, C5, C8, C10, C12, C14, C17, C19, C21, C23, C25, C27, C30, C32, C34, C36, . . . .
By defining any one of the directions of the aforesaid symmetrical surface as a symmetrical surface and setting decentration in the corresponding direction, for instance, setting the direction of the optical system with respect to a symmetrical surface parallel with the Y-Z plane in the Y-axis direction and the direction of the optical system with respect to a symmetrical surface parallel with the X-Z plane in the X-axis direction, it is possible to make effective correction for rotationally asymmetric aberrations produced due to decentration while, at the same time, productivity is improved.
The aforesaid defining equation (a) is merely provided as an example. The present invention has the feature of using a rotationally asymmetric surface having only one symmetric surface thereby correcting rotationally asymmetric aberrations produced due to decentration and, at the same time, improving productivity. However, it is understood that similar effects are obtainable even for any defining equations other than the aforesaid defining equation (a).
In the present invention, the reflecting surface provided at the second prism may be formed in a free-form surface shape symmetrical with respect to plane, which has only one symmetric plane.
The volume hologram (HOE) of the volume hologram element according to the present invention is defined as follows. FIG. 11 is illustrative of the principle for giving a definition of HOE according to the present invention.
First of all, ray tracing of wavelength xcex entering and leaving an HOE plane is given by the following equation (b), using an optical path difference function "PHgr"0 on the HOE plane as defined with respect to the reference wavelength xcex0=HWL.
ndQdxc3x97N=niQixc3x97N+m(xcex/xcex0)∇"PHgr"0xc3x97Nxe2x80x83xe2x80x83(b) 
Here N is the normal vector of the HOE plane, ni (nd) is the refractive index of the entrance (emergence) side, Qi (Qd) is the entrance (emergence) vector (in vector), and m=HOR is the order of diffraction of emergent light.
If the HOE is fabricated (defined) by interference of object light from a two-point light source for the reference wavelength xcex0, i.e., a light source of point P1=(HX1, HY1, HZ1) as shown in FIG. 12 and reference light from a light source of point P2=(HX2, HY2, HZ2), then
"PHgr"0="PHgr"02P=n2xc2x7s2xc2x7r2xe2x88x92n1xc2x7s1xc2x7r1 
where r1 (r2) is the distance ( greater than 0) from point P1 (P2) to given coordinates P on the HOE plane, n1 (n2) is the refractive index of the medium on which the HOE is positioned at the time of fabrication (definition) and the point P1 (P2) is located, and s1=HV1, and s2=HV2 is a symbol for taking the direction of propagation of light into consideration. This symbol is REA=+1 in the case where the light source is a divergent (real point) light source, and VIR=xe2x88x921 in the case where the light source is a convergent (virtual point) light source. In conjunction with the definition of the HOE in lens data, it is noted that the refractive index n1 (n2) of the medium on which the HOE is placed at the time of fabrication (definition) is defined by the refractive index of the side of the medium contiguous to the HOE plane in the lens data, on which the point P1 (P2) is found.
Generally, the reference light and object light used for HOE fabrication are not always limited to spherical waves.
In this case, the optical path difference function"PHgr"0 for the HOE may be expressed in terms of the following equation (c) with the addition thereto of an additive phase term"PHgr"0Poly (an optical path difference function at the reference wavelength xcex0) represented by a polynominal.
"PHgr"0="PHgr"02P+"PHgr"0Polyxe2x80x83xe2x80x83(c) 
Here, the polynominal is                               Φ          0          Poly                =                  xe2x80x83                ⁢                              ∑            j                    ⁢                                    H              j                        ·                          x              m                        ·                          y              n                                                              =                  xe2x80x83                ⁢                                            H              1                        ⁢            x                    +                                    H              2                        ⁢            y                    +                                    H              3                        ⁢                          x              2                                +                                    H              4                        ⁢            x            ⁢                          xe2x80x83                        ⁢            y                    +                                    H              5                        ⁢                          y              2                                +                                                  xe2x80x83                ⁢                                            H              6                        ⁢                          x              3                                +                                    H              7                        ⁢                          x              2                        ⁢            y                    +                                    H              8                        ⁢            x            ⁢                          xe2x80x83                        ⁢                          y              2                                +                                    H              9                        ⁢                          y              3                                +          …                    
In general, this may be defined by
j={(m+n)2+m+3n}/2 
Here, Hj is the coefficient of each term.
For convenience of optical design, the HOE may be defined by representing the optical path difference function"PHgr"0 in terms of the additive term alone, as in the case of
"PHgr"0="PHgr"0Poly 
For instance, if light beams from the two-point light source P1 (P2) are in coincidence with each other, the component"PHgr"02P of the optical path difference function"PHgr"0 by interference is then reduced down to zero. This is tantamount to the case where the optical path difference function is substantially represented by the additive term alone.
All the aforesaid explanation of the HOE holds true for local coordinates using the origin of the HOE as reference.
Exemplified below are the constructive parameters for the definition of the HOE.
In Example 1 given later, the hologram element is defined as composed of only one HOE{circle around (1)} layer that diffracts the red band light with its center at 630-nm wavelength in an angle selective manner. Regarding the HOE for the blue band light with its center at 470-nm wavelength and the HOE for the green band light with its center at 535-nm wavelength, however, no optical path difference function is given. This is because the shape and spacing of interference fringes on the surface of the hologram are the same as those of HOE{circle around (1)} for the red band light, and so is the optical path difference function "PHgr"0 represented by equation (c). It is here noted that the spacings and tilts of the interference fringes in the hologram medium of each HOE differ as a matter of course; the spacings and tilts of the interference fringes in the hologram medium of each HOE at discrete six points in the hologram plane are indicated to show three or the red, green and blue volume holograms.
Still other objects and advantages of the invention will in part be obvious and will in part be apparent from the specification.
The invention accordingly comprises the features of construction, combinations of elements, and arrangement of parts, which will be exemplified in the construction hereinafter set forth, and the scope of the invention will be indicated in the claims.